Linear Algebra II (MST20050)

After sucessful comletion of this module, a student should:1. have a firm understanding of the basic concepts of linear independence and span;2. know how to determine when a subset is a subpace;3. be familiar with several basic results on vector spaces relating bases, subspaces and dimension;4. be able to determine inner products of a vector space;5. know the Cauchy-Schwarz inequality and its corollaries;6. be able to compute that characteristic polynomial and eigenvalues of a matrix and to determine whether or not a matrix can be diagonalized;7. know the rank-nullity theorem and the connection between linear transformations and matrices; 8. be able to apply Gaussian elimination techniques to decide : (a) whether or not a given set of vectors is linear independent; (b) whether a vector is in the span of a set of vectors; (c) whether or not a vector is contained in the column space of a matrix; (d) how to compute the a basis for the column space, row space or null space of a matrix; (e) how to compute a basis for the eigenspace of a matrix for given eigenvalue; (f) how to obtain a matrix representation of a linear transformation.